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A crystal is a solid with long-range spatial order in its constituents. In a periodic crystal, translation by a lattice vector reproduces the structure; a unit cell and its constituent arrangement describe the repeating pattern. The atomic structure is distinct from the visible external shape: an irregularly cut specimen can remain a single ordered crystal.

Diffraction probes that order because radiation scattered from many regularly arranged sites can reinforce at selected directions. The resulting pattern reveals structural spacings and orientation, rather than merely showing the specimen's outer faces. A single crystal maintains one coherent orientation across the specimen, while a polycrystalline material contains many crystal grains. Crystal orientation can make properties anisotropic, so a test along one direction need not predict response along another. Surface shape additionally depends on equilibrium surface free energy and growth kinetics.

The characteristic growth phenomena require an asymmetric material response and a way to retain irreversible change. Low crystal symmetry and directional defect or deformation behaviour make uranium and zirconium important examples, whereas an ideal cubic material has isotropic linear thermal expansion and no symmetry-selected traceless single-crystal growth tensor in an otherwise isotropic environment.

alpha uranium is orthorhombic and has strongly anisotropic thermal response. In a textured polycrystalline material, incompatible crystal grain strains can be accommodated asymmetrically over a thermal cycle and leave macroscopic distortion. The same metal can also show irradiation growth through anisotropic irradiation-defect evolution. zirconium and its hexagonal close-packed alloys are major examples of irradiation growth; their basal and c-axis directions need not acquire the same strain.

Cubic austenitic steel does not exhibit the same intrinsic orientation-driven response merely because it is irradiated. It can nevertheless undergo void swelling, irradiation creep, thermal-stress plasticity or distortion under gradients. Thus absence of this growth mechanism does not imply dimensional stability under all reactor conditions. Conversely, a noncubic crystal is not guaranteed to grow during every thermal cycle: constraints, inelastic accommodation and the microstructure still matter.

A single crystal is a crystalline specimen whose ordered structure has one continuous crystallographic orientation, rather than being divided into differently oriented crystal grains. It can still contain dislocations, impurities and other defects; the term does not mean an absolutely perfect lattice.

A diffraction pattern from one well-oriented specimen resolves its crystallographic directions, while rotating it changes which reflections are observed. Mechanical or thermal measurements along different directions can reveal intrinsic anisotropy that would be averaged over many orientations in a polycrystalline material. The absence of internal grain boundaries also changes transport and deformation mechanisms that depend on those boundaries. A specimen's outline is not the criterion: cutting a piece from a single crystal changes its external shape without necessarily changing its internal crystallographic identity.

Permanent dimensional change accumulated over temperature cycles. anisotropic thermal expansion can create mismatch stresses in a polycrystalline material, but noncancelling irreversible accommodation is needed for net growth; a freely expanding, uniformly heated elastic single crystal returns to its original dimensions.